Nanocomposites of functionalized carbon nanotubes (CNTsf) as nanofillers, and a copolymer of star-shaped poly(ε-caprolactone) (stPCL) and poly(ethylene glycol) (PEG) as a polymeric matrix were synthesized, characterized, and their resistance to the growth of Staphylococcus aureus and Pseudomonas aeruginosa was evaluated. CNTsf contain hydroxyl, carboxyl and acyl chloride groups attached to their surface. Nanocomposites were prepared by mixing CNTsf to a solution of stPCL-PEG copolymer. Raman and FT-IR spectroscopies confirm the functionalization of carbon nanotubes (CNTs). Star-shaped PCL-PEG copolymer was characterized by Gel permeation chromatography (GPC), and 1H-NMR and 13C-NMR spectroscopies. X-ray photoelectron spectroscopy (XPS) shows that CNTsf are grafted to the stPCL-PEG copolymer. Crystallization behavior of the nanocomposites depends on the amount of CNTsf used in their preparation, detecting nucleation (nanocomposites prepared with 0.5 wt.% of CNTsf) or anti-nucleation (nanocomposites prepared with 1.0 wt.% of CNTsf) effects. Young’s Moduli and thermal stability of nanocomposites were higher, but their resistence to the proliferation of Staphylococcus aureus and Pseudomonas aeruginosa was lower than the observed for their pure polymer matrix.